While it is easily feasible to check bags through, UA no longer does by policy because there are massive headaches caused by newish (January 2012) DOT rules which apply the first segment baggage rules to the entire itinerary. If UA checks through, but Qatar only sees the xIAH itinerary when you check in for the return, it can take a long time to sort out. So, the easy answer has become what it is. You are on two separate itineraries, each with their own allowance.

Doesn't mean a kindly CSR won't do it, just that there's a reason behind the "no" if that's what happens.